The Geography of Mars

Surface Temperature, Sun Angle, and Elevation

• to introduce you to Planetary Fourier Spectrometer (PFS) derived data on surface temperatures and to THEMIS and TES derived data on dust
• to give you practice in inferring patterns among factors that partially drive Martian weather
• to give you practice in spreadsheet graphing, using the Column and Line option and standardizing data measured in very different units and magnitudes

The PFS is an instrument on Mars Express, a European Space Agency spacecraft that has been orbiting Mars since early 2004. The PFS became inoperable in late 2005, unfortunately, but has since resumed operation. The PFS carries the Long Wavelength Channel instrument, which collects spectra from a wide array of infrared wavelengths (1.2 - 45 microns). The PFS focusses on:

• identifying minerals in Martian dust
• taking partial pressure measurements for CO₂ (which it does by measuring the 15 micron CO₂ absorption band)
• inferring surface temperatures by noting the peak emission wavelengths from the Martian surface and applying the Wien Displacement Law (L = 2897/T, where L = wavelength in microns and T = temperature in Kelvins)

This last function is the source of the data for this lab, taken from ESA's Mars Express' 399th orbit on 1 May 2006. The data are presented in graphical form each week by the European Space Agency, and I turned the graphical data into tabular data for this lab.

Other instruments on other missions collect data on dust optical depth or tau, or the natural logarithm of the radiant energy received by something (such as Mars' dust) and the radiant energy transmitted by it. Absorption of solar energy by dust increases that ratio. Instruments that capture optical depth include Mars Global Surveyor's Thermal Emission Spectrometer (TES), Mars Odyssey's THermal EMission Imaging System (THEMIS), and Mars Reconnaissance Orbiter's Mars Climate Sounder (MCS). I converted a graph for Mars Year 27 (2005) based on TES and THEMIS in Montabone et al. (2014) into tabular data through interpolation and mathematical smoothing.

Your data

You can download your data from https://home.csulb.edu/~rodrigue/geog441541/labs/PFS/PFStemperature1figure.ods. This is an Open/Libre Office Calc database, which you can save on your portable storage device or on the scratch drive in the lab. Remember the lab scratch drive is normally cleaned out each night, so you do need to transfer your work to your own storage device or e-mail it to yourself.

The data are presented in five columns:

• Latitude (note that southern hemisphere latitudes are given as negative numbers and northern hemisphere latitudes are given as positive numbers)
• MOLA elev (m) is derived from the NASA Mars Orbiter Laser Altimeter and is presented in meters above or below the Martian geoid, which is used there in lieu of mean sea level). These are the mean elevations at all longitudes, IIRC.
• Dust opt dpth is a measure of the amount of absorption by dust, that is, the optical depth or natural logarithm of the amount of incident radiation divided by the amount transmitted to the instrument.
• Sun angle is the angle that the sun makes with the horizon at the point directly below the orbiter (the spacecraft's nadir). This is a function of latitude, the sun's declination (on Mars, that can range from +25° or 25° N to 25° S), and the time of day. I assumed noon around the 40th sol of the martian year (mid-spring in the Northern Hemisphere; mid-autumn in the Southern Hemisphere).
• Sfc Temp K means surface temperatures in Kelvins (the freezing point of water at sea level on Earth is 273 K, and the boiling point is 373 K -- comfortable room temperatures would be 293K - 298 K or so).

We need to get these very disparate measurements aligned onto a common unit of measure so that we can directly compare one to another without having to make four separate graphs. Let's convert elevation, sun angle, dust optical depth, and surface temperature into standard scores. The easiest way to do that is to enter the following formula into cell G7: =STANDARDIZE(C7;C$71;C$73) -- you'll see I've already calculated the mean and standard deviation so all you need to concentrate on is generating the t-scores. The cell should now show -0.448-ish. If so, format it to maybe three or so decimal places of accuracy and then right-click and copy the formula to the end of the data in cell G67. While the standardized elevation data are still highlighted, move your cursor to the lower right corner of the last cell and right-click and drag it to cell J67 and you should now have all your graphable standard scores ready to go.

Graphing the data

Now, highlight cells B5 through B67 and, holding down the Control key, also highlight from cells G5 through J67. Make sure you didn't also highlight the means, medians, etc. at the bottom of the table. Ask for a graph and choose the Column and Line option. In there, choose THREE (3) lines and accept the default (left box). Hit Next. In this dialogue box, click First column as label and hit Next and then Next again. Fill in your title, label the X axis as latitude and the Y axis as t-scores and hit Finish.

You're not out of the woods yet. The X axis needs to be repositioned to cross at Start to bring the label down under the graph and then ask it to Reverse Scale (so the negative or southern latitudes are on the left). That will mess up the Y axis, so format the Y axis to reposition it so that it crosses the other axis at the End (to bring it over to the left side) and you might want to reduce the number of decimal places to maybe 2 to make it less busy. You can pretty it all up with a neat line border and assorted experiments with color.

So, what you have now is a means of directly comparing surface temperatures at that time of year with various possible drivers, such as sun angle, elevation, and dustiness.

Lab report

Your graphs in hand, write a brief lab report answering the following questions. Your lab report should include your graph. It can be turned in during class or deposited in BeachBoard's digital dropbox (Labs: PFS temperatures). Because of the Department's printing budget woes, I'll be okay with this lab going up on BeachBoard without a paper copy.

• Which of the three factors is likely to be the main driver of temperatures on Mars as much as on Earth?
  • Is that what you see in general?
  • What about any anomalies or departures from that relationship? Where do they occur?

• What would you predict the effect of the other factors would be on the core relationship?
  • Do you see any signals in the data that indicate the effect of the other factors?
  • Where? How influential do they seem?